assig7 - 4 Let A = 2-7 1 7 3-8 2 7 1-2-1 3-8 3 7 Find an...

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MATH 245 Linear Algebra 2, Assignment 7 Not to be handed in 1: Find a singular value decomposition A = Q Σ P * for the matrix A = 1 2 2 0 3 1 1 1 . 2: Let A M n × n ( C ) be Hermitian and positive-definite. Show that if A = Q Σ P * is a singular value decompo- sition of A , then Q = P . 3: Find the number of similarity classes of 8 × 8 complex matrices whose distinct eigenvalues are 1 and 2.
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Unformatted text preview: 4: Let A = 2-7 1 7 3-8 2 7 1-2-1 3-8 3 7 . Find an invertible matrix P such that P-1 AP is in Jordan form. 5: Let A = 1 1 0 0 1 1 0 0 1-1 1-1 . (a) Find A n , where n is a positive integer. (b) Find e A = I + A + 1 2! A 2 + 1 3! A 3 + ··· ....
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